Exact solution to the random sequential dynamics of a message passing algorithm

TL;DR

This paper provides an exact analysis of the random sequential dynamics of a message passing algorithm for Ising models, linking stability criteria to convergence behavior in large systems.

Contribution

It derives exact two-time correlation functions and establishes the de Almeida-Thouless criterion as necessary and sufficient for convergence.

Findings

Exact two-time correlation functions derived

de Almeida-Thouless criterion linked to convergence

Convergence conditions established for large systems

Abstract

We analyze the random sequential dynamics of a message passing algorithm for Ising models with random interactions in the large system limit. We derive exact results for the two-time correlation functions and the speed of convergence. The {\em de Almedia-Thouless} stability criterion of the static problem is found to be necessary and sufficient for the global convergence of the random sequential dynamics.